How much air is needed for wind?

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How much air is needed for wind?

Postby King Author » Thu Apr 14, 2011 5:04 pm UTC

I'm reading a scifi book right now that takes place on a massive generation ship travelling to a distant planet.

The ship is a spinning barrel (to give artificial gravity to its inhabitants, who live on the inside). Only about half of the inside of the barrel is covered with grass and trees and such. Half longways (from one circlular end of the barrel to the other), that is. The other half is bare metal and circuits, with an artificial "sun" running the length. Essentially, this sun is a really, really, really, really, really large gas-discharge light. As an aside, whatever gas is excited to make the sun "rise" is "brownish purple" when it's not lit. Any idea what gas that might be?

There are "a couple of hundred" cities in the barrel, all of which live with essentially medieval technology (the inhabitants of this world don't know they're on a generation ship; they think their world is the whole of existence), though there's some significant schizo tech. It's never stated outright, but implied that the cities are significantly well-spaced out (two large ones are explicitly stated to be separated by 172 miles); there's a lot of wilderness inbetween them. Then again, they do have mostly medieval technology (ox carts, human-powered litters) so their perception of distance is doubtlessly not the same as ours.

Each of the "hundreds" of cities is said to have "twelve thousand" sleeping android soldiers at its disposal. Now, this is because the creator of the generation ship, whose choice it was to present their journey as a mystic one to its peoples and keep them in the dark, wanted to transport tons of people to the planet of its ultimate destination, but didn't want any one city to get too powerful, lest a unified government start poking around the ship and discover its mysteries too soon.

The city our tale focuses on has between 585,000 and 1,053,000 residents, and is presented as a rather prosperous city. At least half a dozen other cities are implied to have an equal population. I always assumed most of the rest of the cities are comparably quite small, but they might be equally big, I don't know.

From all this, my estimate is that the grassy, habitable half of this generation ship is between 50 million and 1 billion acres in size.

All this rigamarole is to ask this question -- is a cyllindrical generation ship whose interior is between 100 million and 2 billion acres in size (someone else would have to calculate the length of such a cylinder) large enough to have wind? Will the artificial sun even generate wind in this generation ship? How big does a mass of air have to be to have noticable wind (since all volumes of air have some degree of turbulence)?
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Re: How much air is needed for wind?

Postby broken_escalator » Thu Apr 14, 2011 5:12 pm UTC

That is a really interesting question. Did the ship have any sort of air filtration system that would generate air currents?

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Re: How much air is needed for wind?

Postby Tass » Thu Apr 14, 2011 5:14 pm UTC

It is more than big enough. With that size it is also going to have a near vacuum "space" in the center.

Weather patterns are going to be very strange though. With "suns" at ground level giving massive updraft over the sun panels at day, and a powerful (how powerful depends on the actual size) Coriolis force turned sideways.

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Re: How much air is needed for wind?

Postby King Author » Thu Apr 14, 2011 5:36 pm UTC

There was no air filtration system mentioned, escalator. Oh, right, this is the Book of the Long Sun, by Gene Wolfe, by the way. I always assumed that the ship was big enough that the plentiful grass and trees generated all the oxygen (the ship is literally an inside-out earth in a bottle), that any such filtration would be as unnecessary as filtrating the Earth's air.

Tass, it's funny you mention the center -- completely open airships lazily fly through the center of the generation ship, and they experience I sort of weightlessness there. I presumed that, as such, the entire interior of the generation ship was completely filled with atmosphere, since people are floating around in the sky without aritificial air supplies or anything.
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Re: How much air is needed for wind?

Postby Moose Hole » Thu Apr 14, 2011 5:38 pm UTC

So is it big enough to break wind?

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Re: How much air is needed for wind?

Postby Tass » Thu Apr 14, 2011 5:51 pm UTC

King Author wrote:Tass, it's funny you mention the center -- completely open airships lazily fly through the center of the generation ship, and they experience I sort of weightlessness there. I presumed that, as such, the entire interior of the generation ship was completely filled with atmosphere, since people are floating around in the sky without aritificial air supplies or anything.


Under one g the "half life" (scale height) of atmospheric pressure is about 5km. So to have air enough for an airship it can be no more than some 50km in diameter (pressure in center corresponding to 12.5km on earth). The one you describe would be hundreds. Which incidentally also means that it needs something of theoretical nanotube strength or better to keep the hull together.

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Re: How much air is needed for wind?

Postby King Author » Fri Apr 15, 2011 3:46 pm UTC

Yeah, it's very soft scifi. Never is it even remotely mentioned how the ship was constructed, how its materials were transported onto it, how it propells and aims itself through space to its end destination and, perhaps most glaringly, how it manages to shield its inhabitants from various forms of cosmic radiation.

Can someone do the calculation for certain to tell how big a cyllinder would be if its interior (excluding the circles) is 100 million acres? And if it's 2 billion? I wouldn't even begin to know how.

Also, oh! I know. Someone take a diameter of 50 kilometers, as Tass calculated would be the maximum to have atmosphere completely filling the "cabin" (so to speak), and an interior surface area of 100 million (and, separately, 2 billion) acres and see how long the cyllinder would be in each case.
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Re: How much air is needed for wind?

Postby zmatt » Fri Apr 15, 2011 3:48 pm UTC

what you are describing sounds like an O'Neill Island 3, albeit closed and much larger than projected.
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Re: How much air is needed for wind?

Postby broken_escalator » Fri Apr 15, 2011 3:58 pm UTC

King Author wrote:Also, oh! I know. Someone take a diameter of 50 kilometers, as Tass calculated would be the maximum to have atmosphere completely filling the "cabin" (so to speak), and an interior surface area of 100 million (and, separately, 2 billion) acres and see how long the cyllinder would be in each case.

Hmm, not sure how to use wolframalphafor this situation, but I tried.

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Re: How much air is needed for wind?

Postby Moose Hole » Fri Apr 15, 2011 4:59 pm UTC

Wait, the "sun" is kind of like a ceiling in the center, right? Is it just a thin tube, or is it huge? What I'm getting at is, could the "sun" be hundreds of km in diameter, leaving 50km for air and people and junk?

Separately, what happens when people dig holes?

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Re: How much air is needed for wind?

Postby broken_escalator » Fri Apr 15, 2011 5:09 pm UTC

Yeah, the cylinder would probably need extra buffer space for layers of soil and whatnot. And probably also whatever spaceship-stuff they would need to protect it from the harsh elements in space.

Moose Hole wrote:what happens when people dig holes?

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Re: How much air is needed for wind?

Postby Meteorswarm » Fri Apr 15, 2011 7:09 pm UTC

King Author wrote:how it manages to shield its inhabitants from various forms of cosmic radiation.


To be fair, a quantity of dirt performs this service remarkably well.
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Re: How much air is needed for wind?

Postby WarDaft » Fri Apr 15, 2011 8:14 pm UTC

Heck, air performs it rather well too.


If we presume the cylinder to be 100 km in diameter and 2 billion acres, it has to be about 25000 km long. If we let it be 200 km in diameter and 100 million acres, then it would be about 644 kilometers long.


And traditional estimations of the atmospheres extent will not work - it exists in a distinguishable 'gravity' gradient, the center of the cylinder experiences essentially no artificial gravity, so for 1 atmosphere of pressure at the surface, it might actually depend on being "full" of air, rather than just the air's weight.
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Re: How much air is needed for wind?

Postby Tass » Sat Apr 16, 2011 12:15 am UTC

WarDaft wrote:And traditional estimations of the atmospheres extent will not work - it exists in a distinguishable 'gravity' gradient, the center of the cylinder experiences essentially no artificial gravity, so for 1 atmosphere of pressure at the surface, it might actually depend on being "full" of air, rather than just the air's weight.


Gravity scales linearly with height, so 50km diameter (25km radius) corresponds to a height of 12.5 in the center.

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Re: How much air is needed for wind?

Postby collegestudent22 » Sat Apr 16, 2011 8:36 am UTC

Tass wrote:
WarDaft wrote:And traditional estimations of the atmospheres extent will not work - it exists in a distinguishable 'gravity' gradient, the center of the cylinder experiences essentially no artificial gravity, so for 1 atmosphere of pressure at the surface, it might actually depend on being "full" of air, rather than just the air's weight.


Gravity scales linearly with height, so 50km diameter (25km radius) corresponds to a height of 12.5 in the center.


Presumably, it isn't traditional gravity, though. I would assume that it would be rotational motion producing artificial "gravity", which would change things.

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Re: How much air is needed for wind?

Postby Robert'); DROP TABLE *; » Sat Apr 16, 2011 11:56 am UTC

The whole point of General Relativity is that doesn't change things, AFAIK.
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Re: How much air is needed for wind?

Postby Tass » Sat Apr 16, 2011 2:23 pm UTC

collegestudent22 wrote:I would assume that it would be rotational motion producing artificial "gravity"


Yes.

collegestudent22 wrote:which would change things.


No. No it wouldn't.

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Re: How much air is needed for wind?

Postby collegestudent22 » Wed Apr 27, 2011 9:09 am UTC

Robert'); DROP TABLE *; wrote:The whole point of General Relativity is that doesn't change things, AFAIK.


It wouldn't change the application to anything on the surface, but it would change the effect on things not forced to rotate - like the atmosphere. Fluid dynamics would be different, and gravity wouldn't really even apply to the air. As an example, take a tube of water and hold it horizontally. Then spin it (rather quickly, in order to minimize the effect of Earth gravity due to the larger acceleration due to the spin - or do it in space). Fluid dynamics will affect the water, as the effect of a force on the outer edge pushing inward and in the direction of rotation, but there would be no gravitational force on water that wasn't on the outer edge.

As an answer to the OP, the effects of fluid dynamics would create "wind", although it would not likely result in "weather" in the form of storms, wind variances, etc.

In addition, the observed gravitational acceleration would vary as a function of r (in terms of angular velocity), instead of 1/r2, even without the fact that the acceleration only applies in full to the matter colliding with the rotating surface (which is why if you threw a ball straight up in such an environment, it would actually land a bit further from you in the direction of rotation.)

The "gravity" would be essentially zero in the center due to rotational mechanics, regardless of matter content.

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Re: How much air is needed for wind?

Postby Tass » Wed Apr 27, 2011 10:49 am UTC

collegestudent22 wrote:It wouldn't change the application to anything on the surface, but it would change the effect on things not forced to rotate - like the atmosphere. Fluid dynamics would be different, and gravity wouldn't really even apply to the air. As an example, take a tube of water and hold it horizontally. Then spin it (rather quickly, in order to minimize the effect of Earth gravity due to the larger acceleration due to the spin - or do it in space). Fluid dynamics will affect the water, as the effect of a force on the outer edge pushing inward and in the direction of rotation, but there would be no gravitational force on water that wasn't on the outer edge.

As an answer to the OP, the effects of fluid dynamics would create "wind", although it would not likely result in "weather" in the form of storms, wind variances, etc.

In addition, the observed gravitational acceleration would vary as a function of r (in terms of angular velocity), instead of 1/r2, even without the fact that the acceleration only applies in full to the matter colliding with the rotating surface (which is why if you threw a ball straight up in such an environment, it would actually land a bit further from you in the direction of rotation.)

The "gravity" would be essentially zero in the center due to rotational mechanics, regardless of matter content.


Potato potato. In the rotating frame everything if affected by the centrifugal force. If it moves relative to the cylinder it is merely also affected by a powerful Coriolis force. As I already stated the weather patterns will be very unusual under the influence of this powerful horizontal Coriolis rather than our familiar weak vertical one. It would take extensive simulations to predict how it will behave. Still there is noting to keep the air mass from rotating - on average - along with the cylinder, so in a sufficiently big cylinder there will be a near vacuum in the center.

You should really choose either the rotating frame or the nonrotating frame when contemplating the equations of motion. Saying mixed nonsense things like

collegestudent22 wrote:the fact that the acceleration only applies in full to the matter colliding with the rotating surface (which is why if you threw a ball straight up in such an environment, it would actually land a bit further from you in the direction of rotation.)


Is a surefire way to get confused.

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Re: How much air is needed for wind?

Postby collegestudent22 » Thu Apr 28, 2011 6:40 pm UTC

Tass wrote:
collegestudent22 wrote:It wouldn't change the application to anything on the surface, but it would change the effect on things not forced to rotate - like the atmosphere. Fluid dynamics would be different, and gravity wouldn't really even apply to the air. As an example, take a tube of water and hold it horizontally. Then spin it (rather quickly, in order to minimize the effect of Earth gravity due to the larger acceleration due to the spin - or do it in space). Fluid dynamics will affect the water, as the effect of a force on the outer edge pushing inward and in the direction of rotation, but there would be no gravitational force on water that wasn't on the outer edge.

As an answer to the OP, the effects of fluid dynamics would create "wind", although it would not likely result in "weather" in the form of storms, wind variances, etc.

In addition, the observed gravitational acceleration would vary as a function of r (in terms of angular velocity), instead of 1/r2, even without the fact that the acceleration only applies in full to the matter colliding with the rotating surface (which is why if you threw a ball straight up in such an environment, it would actually land a bit further from you in the direction of rotation.)

The "gravity" would be essentially zero in the center due to rotational mechanics, regardless of matter content.


Potato potato. In the rotating frame everything if affected by the centrifugal force.


Once not in contact with the cylinder, it is no longer in the rotating frame. It maintains the motion of the cylinder, so it would continue to move in a tangential direction (without some self-powering to move itself in another direction), shortly colliding with the wall again. However, the upper atmosphere will not have touched the cylinder, and would therefore have no inertia in the direction of rotation. Air pressure will in fact force it to cycle (as the upper molecules at a higher pressure fill the now lower pressure area beneath them).

Still there is noting to keep the air mass from rotating - on average - along with the cylinder, so in a sufficiently big cylinder there will be a near vacuum in the center.


Inertia keeps the air mass from rotating as you go upward from the surface, except where it is in direct contact with the rotating cylinder. This then simplifies to a fluid dynamics problem. And I have performed experiments identical to the one I proposed that would demonstrate this concept. Spinning a horizontal cylinder of water (which obeys the same laws of fluid dynamics) at a high enough rate so that gravity is virtually ignored (easily enough to do, even with a bucket of water and your arm) will create a vortex, not an evenly spinning mass. There will be virtually no air in the center, and wind at the surface, due to the characteristics of the vortex. This will occur regardless of the size of the cylinder if apparent gravity and air pressure will conform closely to Earth norms.

You should really choose either the rotating frame or the nonrotating frame when contemplating the equations of motion. Saying mixed nonsense things like

collegestudent22 wrote:the fact that the acceleration only applies in full to the matter colliding with the rotating surface (which is why if you threw a ball straight up in such an environment, it would actually land a bit further from you in the direction of rotation.)


Is a surefire way to get confused.


That is based entirely on the non-rotating frame. From a non-rotating frame, the object, while touching the rotating wheel, is also rotating with the same velocity and acceleration. Once it is removed from the wheel, the forces on it are 0 (when the cylinder travels through vacuum) and it has initial velocity tangential to the point it left equal to the tangential velocity of the wheel. This causes it to travel in a straight line (relative to the non-rotating frame) and collide with the wheel shortly afterward, and the cycle begins again. (In truth, this is what is occurring constantly, but on a small enough scale that it is undetectable by the naked eye and simple instruments.)

The Coriolis "force" is the way to get confused. Look, you have even confused yourself! The Coriolis effect is no more a force than "centrifugal" force. It is due merely to inertia, as a result of the fact that once the object leaves contact with the rotating wheel, it is no longer accelerating due to that rotation, and begins moving in a straight line (which happens to collide with the wheel again shortly, and start over again). Taken from the point of view of the rotating reference, it appears the object is following a curved path, and the Coriolis effect accounts for that, but using the non-rotating reference frame, there is no Coriolis effect.

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Re: How much air is needed for wind?

Postby Tass » Thu Apr 28, 2011 8:03 pm UTC

collegestudent22 wrote:The Coriolis effect is no more a force than "centrifugal" force.


Sigh. In the rotating frame both are very real, and makes calculating what happens much easier in many cases, including this one.

I will write a long reply tomorrow. For now I'll have to go sleep and will just leave you with this classic link: http://xkcd.com/123/

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Re: How much air is needed for wind?

Postby jmorgan3 » Fri Apr 29, 2011 2:59 am UTC

collegestudent22 wrote:Inertia keeps the air mass from rotating as you go upward from the surface, except where it is in direct contact with the rotating cylinder.

Let me introduce to my friend viscosity. Viscous fluid behavior is described by the Navier-Stokes Equations. Solving the Navier-Stokes equation in cylindrical coordinates for the steady case of axisymmetric gas inside a rotating cylindrical shell yields the differential equation,
[math]r^2 \frac{\partial^2 u_{\phi}}{\partial r^2}+r\frac{\partial u_{\phi}}{\partial r}-u_{\phi}=0[/math]
, the solution of which is [imath]u_{\phi}=\omega r[/imath]. This means that the air, given long enough to settle, will assume a constant angular velocity throughout the cylinder.

You can see this by placing water in a vertical cylinder and spinning it at a constant rate. After it has settled, the water will match the cylinder's angular velocity, and spin as if a solid body.

EDIT:
Incidentally, with the solid-body velocity profile, the the density in the middle of the cylinder will be
[math]\rho_{center}=\rho_{surface}*e^{\frac{-gr}{2RT}}[/math]
where [imath]\rho[/imath] is density, g is apparent surface gravity, r is the cylinder radius, R is the specific gas constant (287J/kg/K) for air, and T is the temperature. This assumes an ideal gas and constant temperature. The formula gives a center density of .28kg/m^3 for a 50km diameter cylinder with sea-level standard conditions at the surface. This equates to a density-altitude in the center of 12.7km.
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Re: How much air is needed for wind?

Postby Tass » Fri Apr 29, 2011 3:13 pm UTC

collegestudent22 wrote:Once not in contact with the cylinder, it is no longer in the rotating frame.


You don't understand the concept of a frame, that is how we look at things no matter how they move. Equations of motion can be solved perfectly in a rotating frame even if the stuff you look at is not moving in a circular motion. Centrifugal and Coriolis forces correct for the fact that your frame or coordinate system is not inertial. There is nothing inherently wrong or superior with using the inertial or the rotating system, you are welcome to keep using nonrotating. I just find the rotating system easier when most movement is only a small pertubation from the general rotation. In any case saying that one system is no longer valid when some stuff is not touching some other stuff is complete nonsense.

collegestudent22 wrote:owever, the upper atmosphere will not have touched the cylinder, and would therefore have no inertia in the direction of rotation. Air pressure will in fact force it to cycle (as the upper molecules at a higher pressure fill the now lower pressure area beneath them).


Covered by jmorgan.

collegestudent22 wrote:Inertia keeps the air mass from rotating as you go upward from the surface, except where it is in direct contact with the rotating cylinder. This then simplifies to a fluid dynamics problem. And I have performed experiments identical to the one I proposed that would demonstrate this concept. Spinning a horizontal cylinder of water (which obeys the same laws of fluid dynamics) at a high enough rate so that gravity is virtually ignored (easily enough to do, even with a bucket of water and your arm) will create a vortex, not an evenly spinning mass. There will be virtually no air in the center, and wind at the surface, due to the characteristics of the vortex. This will occur regardless of the size of the cylinder if apparent gravity and air pressure will conform closely to Earth norms.


Sure, when you abruptly start it. It will, however, settle in minutes into a uniform rotation.

collegestudent22 wrote:That is based entirely on the non-rotating frame. From a non-rotating frame, the object, while touching the rotating wheel, is also rotating with the same velocity and acceleration. Once it is removed from the wheel, the forces on it are 0 (when the cylinder travels through vacuum) and it has initial velocity tangential to the point it left equal to the tangential velocity of the wheel. This causes it to travel in a straight line (relative to the non-rotating frame) and collide with the wheel shortly afterward, and the cycle begins again. (In truth, this is what is occurring constantly, but on a small enough scale that it is undetectable by the naked eye and simple instruments.)


Okay fair enough. You are free to use the inertial frame if fictitious forces are to weird for you. But good luck solving fluid dynamics when every piece of air mass is doing an almost circular motion under the force of the differential pressure on the outerside and innerside of it, when the small deviations from circular motion is really what is interesting concerning cylinder weather. I still don't get what you meant by the "in full" in:

collegestudent22 wrote:the fact that the acceleration only applies in full to the matter colliding with the rotating surface (which is why if you threw a ball straight up in such an environment, it would actually land a bit further from you in the direction of rotation.)


Things accelerate when they are under the effect of a force, whether it be collision with a wall, gravity or hydrodynamic forces.

collegestudent22 wrote:Taken from the point of view of the rotating reference, it appears the object is following a curved path, and the Coriolis effect accounts for that, but using the non-rotating reference frame, there is no Coriolis effect.


This is of course correct but for the following non-sequitor:

collegestudent22 wrote:The Coriolis "force" is the way to get confused. Look, you have even confused yourself! The Coriolis effect is no more a force than "centrifugal" force.


... I refer to my previous post as well as the fact that they actually are real physical forces in general relativity, as real as magnetism in electrodynamics.

Finally I will just note that you never hear a weather report saying that the air moves westwards at about 1000mph and is accelerating downwards at 0.01g.

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Re: How much air is needed for wind?

Postby collegestudent22 » Fri Apr 29, 2011 3:43 pm UTC

Tass wrote:
collegestudent22 wrote:Once not in contact with the cylinder, it is no longer in the rotating frame.


You don't understand the concept of a frame, that is how we look at things no matter how they move. Equations of motion can be solved perfectly in a rotating frame even if the stuff you look at is not moving in a circular motion. Centrifugal and Coriolis forces correct for the fact that your frame or coordinate system is not inertial. There is nothing inherently wrong or superior with using the inertial or the rotating system, you are welcome to keep using nonrotating. I just find the rotating system easier when most movement is only a small pertubation from the general rotation. In any case saying that one system is no longer valid when some stuff is not touching some other stuff is complete nonsense.


Right. I did phrase that strangely. I meant to say that after leaving contact with the cylinder, inertial motion is now in a straight line relative to the non-rotating frame.

collegestudent22 wrote:Inertia keeps the air mass from rotating as you go upward from the surface, except where it is in direct contact with the rotating cylinder. This then simplifies to a fluid dynamics problem. And I have performed experiments identical to the one I proposed that would demonstrate this concept. Spinning a horizontal cylinder of water (which obeys the same laws of fluid dynamics) at a high enough rate so that gravity is virtually ignored (easily enough to do, even with a bucket of water and your arm) will create a vortex, not an evenly spinning mass. There will be virtually no air in the center, and wind at the surface, due to the characteristics of the vortex. This will occur regardless of the size of the cylinder if apparent gravity and air pressure will conform closely to Earth norms.


Sure, when you abruptly start it. It will, however, settle in minutes into a uniform rotation.


Fair enough. I was looking at the system in a transient stage, not steady-state.

I still don't get what you meant by the "in full" in:

collegestudent22 wrote:the fact that the acceleration only applies in full to the matter colliding with the rotating surface (which is why if you threw a ball straight up in such an environment, it would actually land a bit further from you in the direction of rotation.)


Things accelerate when they are under the effect of a force, whether it be collision with a wall, gravity or hydrodynamic forces.


The acceleration [caused by the cylinder] is going to create more force when in contact with the object than the air does when it is not, but the air does create some force from the rotation (the wind, as it were). Were there no air, no force would apply once the object is not colliding with the surface, as gravity (in terms of spatial bodies) is negligible.

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Re: How much air is needed for wind?

Postby zerkrox » Sat Apr 30, 2011 11:21 am UTC

How much air do you have? That and pressure differences.

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Re: How much air is needed for wind?

Postby HarvesteR » Fri May 13, 2011 2:06 pm UTC

I'm pretty sure on a volume that large, there would not only be wind, but many other weather effects as well.

NASA's Vehicle Assembly Building in Kennady Space Center, is the largest (in volume) building in the world, and micro weather phenomena have been observed inside it's volume.

So it's pretty much a given that on such a large ship there will be wind. IDK about it's proportions (how wide is it compared to it's length), but it should be pretty safe to assume there will not only be wind, there will be rain and clouds too (provided the atmosphere isn't too tightly controlled by the ship's systems).

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